Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)


Electrical Engineering


The main objective of this thesis is to determine and compare the classification error probabilities of several nonparametric methods to parametric ones in practical or near practical conditions using computer simulation. The usefulness of the Asymptotic Relative Efficiency (ARE) is also observed. The ARE is used to compare one algorithm with another in the limit case conditions which are far from practical circumstances. Details of the ARE concept is given in Chapter II and some of the literatures. The next objective is the investigation of the complexity of the several algorithms studied. Many investigators are implementing their algorithms on computers, and since the computer time is determined by the complexity of the algorithm, a very crucial aspect of any algorithm is its complexity. If the data are processed by other than computer, the hardware of the system required will become more expensive and complicated as the calculation gets more complex. In this respect, the calculation problem is studied. The previously stated objectives are performed extensively with two-class problems, but the actual classification problem in imagery recognition usually is a multi-class one. Hence, the generalization of the two-class problem to the multi-class one is studied as a minor objective. One of the important aspects of this work is that the performance of each algorithm with various data distribution conditions can be found in very practical, not theoretical, circumstances. The adoption of a method as a data processing algorithm by a designer of the system can be based more positively on the results of this work. The merits and the limitations of the nonparametric methods are also determined by the actual handling of data through each method. The effects of sample sizes and signal-to-noise ratios on error probabilities are experimented to give more insight into the algorithm and to see various situational behavior of the method. Through the experiments, determining a nonparametric threshold happens to be an important matter in actual applications of algorithms. This is also studied, and a specific result is drawn.

Library of Congress Subject Headings

Nonparametric statistics



Number of Pages



South Dakota State University